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Fig 1.

Route for bays29 output by ABSQL algorithm.

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Fig 2.

Optimal route of bays29.

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Fig 3.

The optimal route of Berlin52 output by ABSQL algorithm.

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Fig 4.

The optimal route of Tsp225 output by ABSQL algorithm.

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Fig 5.

The optimal route of Berlin52 output by DSRABSQL algorithm.

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Fig 5 Expand

Fig 6.

The optimal route of Tsp225 output by DSRABSQL algorithm.

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Table 1.

Simulation parameters for the QL, ABSQL and DSRABSQL algorithms.

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Table 1 Expand

Table 2.

Results of proposed algorithms and algorithms in [9] for 18 instances.

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Fig 7.

min, avg, max and Std of ch150 obtained by three algorithms.

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Fig 8.

min, avg, max and Std for rat575 obtained by three algorithms.

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Fig 9.

min, avg, max and Std of fl1400 obtained by three algorithms.

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Fig 10.

The value of Nmin for ch150, rat575 and fl1400 obtained by three algorithms.

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Table 3.

Sample frequency contingency table of Nmin and It.

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Table 4.

Sc and rank of DSRABSQL and VDWOA algorithms in G1.

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Table 5.

Sc and rank of DSRABSQL and VDWOA algorithm in G2.

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Fig 11.

The Nmin of DSRABSQL and VDWOA algorithms obtained by testing kroa100, ch150, d198, fl417 50 times, respectively.

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Fig 12.

Boxplots obtained by testing ch150 for 50 times by each algorithm.

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Fig 13.

Boxplots obtained by testing rat575 for 20 times by each algorithm.

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Fig 14.

Boxplots obtained by testing fl1400 for 10 times by each algorithm.

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Table 6.

Table of relationships between algorithms and five strategies for two experimental groups.

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Table 7.

Sc of ch150, rat575 and fl1400 for algorithms of each group.

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Table 8.

The difference of Sc between stgy_5 and stgy_1~ stgy_4 under collaboration or not.

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Table 9.

The min obtained by DSRABSQL, S2V-DQN and 2-opt-DRL algorithms for 25 instances.

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